RDP 8401: The Equations of the RBA82 Model of the Australian Economy III. The Fit of the Model

J.G. Fahrer, R.W. Rankin and J.C. Taylor

August 1984

The parameters of RBA82 are estimated from a log-linear discrete-time approximation to the original model,[17] using quarterly data from 1959(3) to 1980(4). The full twenty-nine equation system is estimated simultaneously using the FIML package RESIMUL developed by Wymer (1968).

A measure of the goodness of fit of the model as a complete system is given by the Carter-Nagar system R2, which is 0.6501; the chi-square test rejects the hypothesis that the model is not consistent with the data.[18]

Table 1 shows the fit of the equations of the model as estimated, in dynamic simulation over two sample periods.[19] It is clear that the model performs well throughout, and is noticeably better for price variables (except export prices) over the shorter period of 1974–1980.

TABLE 1: MEASURES OF FIT, LINEARISED RBA82 MODEL
  RMSE* RMSE*
1959(4)–80(4) 74(1)–80(4)
log d 2.05 2.62
k .30 .29
log Kh 1.06 1.33
log x 4.85 4.22
log i 7.00 7.22
log y 2.65 2.42
log P 4.56 2.59
log Px 6.60 8.61
log Pg 4.82 3.05
log w 3.83 1.71
l .43 .43
log N .80 .46
log B 6.95 6.32
log F 10.61 7.06
log A 5.36 3.55
log T11 9.99 6.66
rb1 .73 1.01
ra .63 .92
rm .78 .96
rb .79 .96
log E 5.27 5.88
log R 17.72 15.43
log C 3.70 2.49
log M 2.76 3.28
lov V 5.01 4.03
log Se 1.93 2.16
log Spe 2.20 2.45
log K 3.83 3.07
log L 1.47 1.56
* ×102. For variables in logarithms, the RMSE is approximately equal to the Root Mean Squared Percentage Error of the original variables (d, Kh, x, i, …).

An additional perspective on the fit of RBA82 is given by Table 2, which compares the RMSE of key equations of RBA76 and RBA84.[20]

TABLE 2: COMPARISON OF ROOT MEAN SQUARE ERRORS, RBA76 AND RBA82
(LINEARISED MODELS)
  RMSE* 1963(2) – 1974(4)
RBA76 RBA82
log d 2.62 0.90
k 0.27 0.30
log x 8.01 4.27
log i 6.66 6.19
log y 3.14 1.88
log P 3.28 4.68
log W 3.98 4.65
log L 0.81 0.80
log R 22.21 20.63
log M 7.77 1.73
log v 12.62 4.12
* ×102

RBA82 outperforms RBA76 in almost all cases. The exceptions are wages and prices; Table 1 suggests that the fit of RBA82 for these variables is better in the late 1970s. It is quite possible that RBA76 would perform poorly, relative to RBA82, if simulated beyond the end of 1974.

Similarly, RBA82 would be of limited usefulness in simulations into the 1980s since the structure of the economy (and of the financial system in particular) has changed considerably. The model would need to be altered to allow for floating exchange and bond rates, and policy reaction functions for exchange intervention and bond tender sizes, as well as shifts in private sector behaviour brought about by these changes in policy structure. Re-estimation, using the systems estimation technique favoured to date in the RBII project, is not feasible due to lack of data, and alternative methods using simulation models (not directly estimated in the traditional way) must be explored. It is envisaged that the major application of the RBA82 structure as outlined in this paper will be as the starting point from which such models are developed.

Footnotes

The techniques used are detailed in Appendix 2. [17]

The system R2 has the same interpretation as traditional single-equation R2 measures, and the chi-square test rejects the null hypothesis that the true system R2 is zero. See Carter and Nagar (1977). [18]

The full period is 1959(4)–1980(4); the first quarter is used to initialise the simulation. [19]

The simulation period 1963(2)–1974(4) was that reported for RBA76 in Jonson, Moses and Wymer (1976), from where the first column is taken. [20]